The seventh volume of Russell’s Collected Papers contains the core of a book which he never completed. He stopped working on it, probably because he felt that he could not honestly go on. He had hoped that Wittgenstein would approve of what he had been writing, but when they met in May 1913, Wittgenstein told him that it was all wrong, and, as Russell admitted to Ottoline Morrell, he did not know how to answer Wittgenstein’s objections. He never published the whole of what he had written, and it is likely that what he did publish was the part that did not particularly interest Wittgenstein, while he suppressed the part on which the fire of Wittgenstein’s criticisms had been concentrated.

The confrontation must have been a scene of a kind that seldom occurs in the history of philosophy – brief and decisive. Russell had been looking forward to collaborating with Wittgenstein, who had arrived in Cambridge the year before in order to learn the philosophy of mathematics from him. It soon became clear that, if they worked together, it would be as equals rather than as tutor and pupil. When Russell showed Wittgenstein the book that he was writing, Wittgenstein produced for his inspection a manuscript of a very different character, Notes on Logic. Russell’s book is obviously a product of the English intellectual establishment and the line of his argument is smooth, flowing and confident, while Wittgenstein’s writing is more staccato and inspirational, a disclosure of thoughts shaped by a different tradition.

They disagreed about a fundamental problem in the theory of language. Many words get their meanings by tagging things in the way that names tag them. How, then, is it that some combinations of these words make sense while others do not? It is easy enough to produce examples of both kinds of combination, but quite another matter to produce a theory about them. The situation is typical of philosophy: we are confronted by an end-game problem and there do not seem to be enough pieces left on the board for its solution. To theorise is to make an explanatory move, but in this case it does not look as if there is anywhere to go.

Russell was a realist, and his instinctive response to this sort of difficulty was to invoke a new kind of thing. Now if he had been doing science, there would have been an agreed way of establishing the existence of a thing of a new kind. But it was not science and he had to appeal to the same realist instinct in us. Of course, we must be careful not to go too far in multiplying entities: our sense of reality must be what he called ‘robust’. But the real question here is whether our so-called sense of reality is anything more than a shared taste for a certain style of explanation.

What has to be explained is the evident fact that only certain combinations of words make sense. It is immediately plausible, but no real advance, to suggest that the reason is that the things tagged by them can be combined in corresponding ways in reality. The difficulty begins when we ask how such possibilities exist in the nature of things. Russell’s first step is to bring in the concept of structure. When a possibility is realised, we have an actual structure. That is simply a geometrical way of saying that we have a fact. His theory begins to gather momentum when he points out, quite correctly, that the possibility of the structure existed before it was realised. He then calls this possibility a ‘form’, and he claims that nature contains not only things tagged by words but also forms, which he saw as a set of stencils into which things can be slotted.

Because this is not science, we need to be told something about the character and status of forms and about the way in which we become aware of them. This was the point of divergence between Russell and Wittgenstein in 1913. Russell believed that our awareness of them is very like our awareness of the things whose structured combinations exemplify them and he used the same term in both cases, ‘acquaintance’. The only difference that he saw was that acquaintance with a form involved the knowledge that there was at least one actual structure exemplifying it. Wittgenstein took the opposite view: our awareness of forms is nothing like our awareness of the things combined in the structures that exemplify them. To be aware of a form is to understand a possibility, which is something dynamic, but the ultimate constituents of the world are logical atoms, things which have no structure and, therefore, cannot be understood but only tagged with names and identified.